The metric space of geodesic laminations on a surface: I

Abstract

We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric $d_H$ and with a variation of this metric called the $d_{log}$ metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also relate these two metrics to another metric which is combinatorially defined in terms of train tracks.